Factor Review: Mastering Algebra through Multiplication and Factoring Techniques
This guide focuses on the essential techniques for factoring algebraic expressions, particularly in understanding the relationship between multiplication and factoring. It covers the step-by-step process of factoring trinomials, utilizing the Greatest Common Factor (GCF), and applying methods like splitting the middle term and factoring by grouping. Additionally, it explores key concepts such as the difference of squares and quadratic expressions. Perfect for students looking to enhance their algebra skills and comprehension of polynomial factorization.
Factor Review: Mastering Algebra through Multiplication and Factoring Techniques
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Presentation Transcript
Factor Review Algebra B
Multiplying a(b + c) ab + ac Factoring Factoring expressions Factoring an expression is the opposite of multiplying. Often: When we multiply an expression we remove the parentheses. When we factor an expression we write it with parentheses.
a2 + 3a + 2 Factoring Factoring expressions Factoring an expression is the opposite of multiplying. Multiplying (a + 1)(a + 2) Often: When we multiply an expression we remove the parentheses. When we factor an expression we write it with parentheses.
Then, look at the remaining factor. • If it is Linear, you are done factoring.
Then, look at the remaining factor. Difference of Squares a2 – b2 = (a-b)(a+b) Is it Quadratic? If it is a: yes Trinomial Calculate the discriminant b2 – 4ac. Is it square? yes Trinomial where a = 1 Find factors of c that add to b. yes no Trinomial where a 1 Find factors of ac that add to b. Split the middle term and then factor by grouping. Can’t be factored more
Remember: • First factor out GCF if there is one • Remember: Multiply to last term add to middle. • ax2+bx+c=( + )( + )ax2-bx+c = ( - )( - )ax2bx-c = ( + )( - ) • If you are using split the middle, split the linear term into two linear terms
Or Split the Middle Term: Steps Factor out GCF if there is one. Identify abc Multiply ac Find factors of (ac) that add up to b Split bx into two terms Factor by grouping
Factoring trinomials of form: Splitting the middle term Steps Factor out GCF if there is one. Identify abc Multiply ac Find factors of (ac) that add up to b Split bx into two terms Factor by grouping No GCF a=6b=-5c=-4 ac = 6(-4)=-24 -8 and 3 Which factors of -24 add up to -5?
Or Another way to split the middle • Factor 2x2 + x - 6 • Multiply a and c together. 2∙(-6) = -12 • Find factors of ac that add up to b. -3 and 4 • Fill in a box as shown:
2x -3 • Factor 2x2 + x – 6 • Factor out the common factor from the top row and place it beside the box next to the first term. • Factor out the common factor from the bottom row and place it beside the box next to the “other factor.” • Factor out the common factor from the left column and place it on top of the box above the first term. • Factor out the common factor from the right column and place it on top of the box above the “one factor.” • Put together your answer. x +2 (x+2)(2x-3)
Is it Cubic or a higher degree 4-Term Polynomial Try to factor by grouping. If it is a: yes
Factoring by grouping Factor a3+ a2+ 4a + 4 Two terms share a common factor of a2and the remaining two terms share a common factor of 4. a3 + a2+ 4a + 4 =a3 + a2+ 4a+ 4 = a2(a+ 1) + 4(a+ 1) a2(a + 1) and+ 4(a + 1)share a common factor of (a + 1) so we can write this as (a + 1)(a2+ 4)
